Data transmitting and receiving method using phase shift based precoding and transceiver supporting the same

ABSTRACT

A method for performing a precoding based on a generalized phase shift or a precoding based on an extended phase shift in a Multi-Input Multi-Output (MIMO) system employing several sub-carriers, and a transceiver for supporting the same are disclosed. A phase-shift-based precoding matrix is generalized by multiplying a diagonal matrix for a phase shift by a unitary matrix for maintaining orthogonality between sub-carriers. In this case, a diagonal matrix part may be extended by multiplying a precoding matrix for removing interference between sub-carriers by a diagonal matrix for a phase shift. By generalization and extension of the phase-shift-based precoding, a transceiver is more simplified, and communication efficiency increases.

CROSS-REFERENCE TO RELATED APPLICATIONS

Pursuant to 35 U.S.C. §120, this application claims the benefit ofearlier filing date and right of priority to U.S. ProvisionalApplication Ser. No. 60/889,891 filed on Feb. 14, 2007, U.S. ProvisionalApplication Ser. No. 60/894,665 filed on Mar. 13, 2007, U.S. ProvisionalApplication Ser. No. 61/021,621 filed on Jan. 16, 2008 and U.S.Provisional Application Ser. No. 61/023,437 filed on Jan. 25, 2008, thecontents of which is hereby incorporated by reference herein in theirentirety.

Pursuant to 35 U.S.C. §119(a), this application claims the benefit ofearlier filing date and right of priority to Korean Patent ApplicationNo. 10-2007-0037008, filed on Apr. 16, 2007, Korean Patent ApplicationNo. 10-2007-0042717, filed May 2, 2007, Korean Patent Application No.10-2007-0051579, filed May 28, 2007 and Korean Patent Application No.10-2007-0095279, filed on Sep. 19, 2007, the contents of which is herebyincorporated by reference herein in their entirety.

TECHNICAL FIELD

The present invention relates to a method for transmitting and receivingdata by performing a precoding based on a generalized phase shift in aMulti-Input Multi-Output (MIMO) system using a plurality ofsub-carriers, and a transceiver for supporting the same.

BACKGROUND ART

In recent times, with the increasing development of informationcommunication technologies, a variety of multimedia services, and avariety of high-quality services have been developed and introduced tothe market, so that demands of wireless communication services arerapidly increasing throughout the world. In order to actively cope withthe increasing demands, capacity of a communication system must beincreased.

A variety of methods for increasing communication capacity underwireless communication have been considered, for example, a method forsearching for a new available frequency band in all frequency bands, anda method for increasing efficiency of limited resources. Asrepresentative examples of the latter method, a transceiver includes aplurality of antennas to guarantee an additional space utilizingresources so that a diversity gain is acquired, or MIMO communicationtechnologies for increasing transmission capacity by transmitting datavia individual antennas in parallel have been developed by manycompanies or developers.

Particularly, a Multiple-Input Multiple-Output (MIMO) system based on anOrthogonal Frequency Division Multiplexing (OFDM) from among the MIMOcommunication technologies will hereinafter be described with referenceto FIG. 1.

FIG. 1 is a block diagram illustrating an OFDM system equipped withmultiple transmission/reception (Tx/Rx) antennas.

Referring to FIG. 1, in a transmission end, a channel encoder 101attaches a redundant bit to a Tx data bit to reduce a negative influenceof a channel or noise. A mapper 103 converts data bit information intodata symbol information. A serial-to-parallel (S/P) converter 105converts the data symbol into a parallel data symbol so that theparallel data symbol can be loaded on several sub-carriers. A MIMOencoder 107 converts the parallel data symbol into space-time signals.

In a reception end, a MIMO decoder 109, a parallel-to-serial (P/S)converter 111, a demapper 113, and a channel decoder 115 have functionsopposite to those of the MIMO encoder 107, the S/P converter 105, themapper 103, and the channel encoder 101 in the transmission end.

Various techniques are required for a MIMO-OFDM system to enhance datatransmission reliability. As a scheme for increasing a spatial diversitygain, there is space-time code (STC), cyclic delay diversity (CDD) orthe like. As a scheme for increasing a signal to noise ratio (SNR),there is beamforming (BF), precoding or the like. In this case, thespace-time code or the cyclic delay diversity scheme is normallyemployed to provide robustness for an open-loop system in which feedbackinformation is not available at the transmitting end due to fast timeupdate of the channel. In other hand, the beamforming or the precodingis normally employed in a closed-loop system in order to maximize asignal to noise ratio by using feedback information which includes aspatial channel property.

As a scheme for increasing a spatial diversity gain and a scheme forincreasing a signal to noise ratio among the above-mentioned schemes,cyclic delay diversity and precoding are explained in detail as follows.

When a system equipped with multiple Tx antennas transmits OFDM signals,the CDD scheme allows the antennas to transmit the OFDM signals havingdifferent delays or amplitudes, so that a reception end can acquire afrequency diversity gain.

FIG. 2 is a block diagram illustrating a transmission end of a MIMOsystem based on the CDD scheme.

Referring to FIG. 2, an OFDN symbol is distributed to individualantennas via the S/P converter and the MIMO encoder, a Cyclic Prefix(CP) for preventing an interference between channels is attached to theOFDM symbol, and then the resultant OFDM symbol with the CP istransmitted to a reception end. In this case, a data sequencetransmitted to a first antenna is applied to the reception end withoutany change, and the other data sequence transmitted to a second antennais cyclic-delayed by a predetermined number of samples as compared tothe first antenna, so that the cyclic-delayed data sequence istransmitted to the second antenna.

In the meantime, if the CDD scheme is implemented in a frequency domain,a cyclic delay may be denoted by a product (or multiplication) of phasesequences. A detailed description thereof will hereinafter be describedwith reference to FIG. 3.

FIG. 3 is a block diagram illustrating a transmission end of a MIMOsystem based on a conventional phase shift diversity (PSD) scheme.

Referring to FIG. 3, different phase sequences (Phase Sequence 1˜PhaseSequence M) of individual antennas are multiplied by individual datasequences in a frequency domain, an Inverse Fast Fourier Transform(IFFT) is performed on the multiplied result, and the IFFT-multiplieddata is transmitted to a reception end. The above-mentioned method ofFIG. 3 is called a phase shift diversity scheme.

In the case of using the phase shift diversity scheme, a flat fadingchannel may be changed to a frequency-selective channel, a frequencydiversity gain may be acquired by a channel encoding process, or amulti-user diversity gain may be acquired by a frequency-selectivescheduling process.

In the meantime, if a closed-loop system includes finite feedbackinformation, two precoding schemes may be used, i.e., a codebook-basedprecoding scheme and a scheme for quantizing channel information andfeeding back the quantized channel information. The codebook-basedprecoding scheme feeds back an index of a precoding matrix, which hasbeen recognized by transmission/reception ends, to thetransmission/reception ends, so that it can acquire a SNR gain.

FIG. 4 is a block diagram illustrating the transmission/reception endsof a MIMO system based on the codebook-based precoding.

Referring to FIG. 4, each of the transmission/reception ends has afinite precoding matrix (P₁-P_(L)). The reception end feeds back anoptimum precoding matrix index (l) to the transmission end using channelinformation, and the transmission end applies a precoding matrixcorresponding to the feedback index to transmission data (X₁˜X_(Mt)).For reference, the following Table 1 shows an exemplary codebook usedwhen feedback information of 3 bits is used in an IEEE 802.16e systemequipped with two Tx antennas to support a spatial multiplex rate of 2.

TABLE 1 Matrix Index (binary) Column 1 Column 2 000 1    0    0    1   001 0.7940 −0.5801 − j0.1818 −0.5801 + j0.1818 −0.7940 010 0.7940 0.0579− j0.6051   0.0579 + j0.6051 −0.7940 011 0.7941 −0.2978 + j0.5298−0.2978 − j0.5298 −0.7941 100 0.7941   0.6038 − j0.0689   0.6038 +j0.0689 −0.7941 101 0.3289   0.6614 − j0.6740   0.6614 + j0.6740 −0.3289110 0.5112   0.4754 + j0.7160   0.4754 − j0.7160 −0.5112 111 0.3289−0.8779 + j0.3481 −0.8779 − j0.3481 −0.3289

The above-mentioned phase-shift diversity scheme can acquire afrequency-selective diversity gain in an open loop, and can acquire afrequency scheduling gain in a closed loop. Due to these advantages ofthe phase-shift diversity scheme, many developers are conductingintensive research into the phase-shift diversity scheme. However, thephase-shift diversity scheme has the spatial multiplexing rate of 1, sothat it cannot acquire a high transfer rate. And, if a resourceallocation is fixed, the phase-shift diversity scheme has difficulty inacquiring the frequency-selective diversity gain and the frequencyscheduling gain.

The codebook-based precoding scheme can use a high spatial multiplexingrate simultaneously while requiring a small amount of feedbackinformation (i.e., index information), so that it can effectivelytransmit data. However, since it must guarantee a stable channel for thefeedback information, it is inappropriate for a mobile environmenthaving an abruptly-changed channel and can be available for only aclosed-loop system.

DISCLOSURE [Technical Problem]

Accordingly, the present invention is directed to a phase-shift-basedprecoding method and a transceiver for supporting the same thatsubstantially obviate one or more problems due to limitations anddisadvantages of the related art.

An object of the present invention is to provide a phase-shift-basedprecoding method for solving the problems of the phase shift diversityscheme and the precoding scheme, and a method for applying thephase-shift-based precoding scheme in various ways by generalizing orextending a phase-shift-based precoding matrix.

Additional advantages, objects, and features of the invention will beset forth in part in the description which follows and in part willbecome apparent to those having ordinary skill in the art uponexamination of the following or may be learned from practice of theinvention. The objectives and other advantages of the invention may berealized and attained by the structure particularly pointed out in thewritten description and claims hereof as well as the appended drawings.

[Technical Solution]

To achieve these objects and other advantages and in accordance with thepurpose of the invention, an aspect of the present invention, there isprovided a method for transmitting a data in a Multi-Input Multi-Output(MIMO) system using a plurality of sub-carriers, the method comprising:determining a precoding matrix as a part of a phase-shift-basedprecoding matrix, determining a first diagonal matrix for a phase shiftas a part of the phase-shift-based precoding matrix, determining aunitary matrix as a part of the phase-shift-based precoding matrix andprecoding by multiplying the phase-shift-based precoding matrix by atransmission symbol per resource, wherein the phase-shift-basedprecoding matrix is determined by multiplying the precoding matrix, thefirst diagonal matrix, and the unitary matrix.

In another aspect of the present invention, there is provided atransceiver for transmitting a data in a Multi-Input Multi-Output (MIMO)system using a plurality of sub-carriers, the transceiver comprising: aprecoding-matrix decision module which determines a precoding matrix asa part of a phase-shift-based precoding matrix, determines a firstdiagonal matrix for a phase shift as a part of the phase-shift-basedprecoding matrix, determines a unitary matrix as a part of thephase-shift-based precoding matrix, and determines the phase-shift-basedprecoding matrix by multiplying the precoding matrix, the first diagonalmatrix, and the unitary matrix and a precoding module for precoding bymultiplying the phase-shift-based precoding matrix by a transmissionsymbol per resource.

In another aspect of the present invention, there is provided a methodfor receiving a data in a Multi-Input Multi-Output (MIMO) system using aplurality of sub-carriers, the method comprising: determining aprecoding matrix as a part of a phase-shift-based precoding matrix,determining a first diagonal matrix for a phase shift as a part of thephase-shift-based precoding matrix, determining a unitary matrix as apart of the phase-shift-based precoding matrix and decoding atransmission symbol per resource based on the phase-shift-basedprecoding matrix, wherein the phase-shift-based precoding matrix isdetermined by multiplying the precoding matrix, the first diagonalmatrix, and the unitary matrix.

In another aspect of the present invention, there is provided a methodfor receiving a data in a Multi-Input Multi-Output (MIMO) system using aplurality of sub-carriers, the method comprising: determining aprecoding matrix as a part of a phase-shift-based precoding matrix,determining a first diagonal matrix for a phase shift as a part of thephase-shift-based precoding matrix, determining a unitary matrix as apart of the phase-shift-based precoding matrix and decoding atransmission symbol per resource based on the phase-shift-basedprecoding matrix, wherein the phase-shift-based precoding matrix isdetermined by multiplying the precoding matrix, the first diagonalmatrix, and the unitary matrix.

The transmitting and receiving methods and transceiver according toabove mentioned aspects, the precoding matrix may be selected to becyclic-repeated in a first codebook according to the resource index (k).

The precoding matrix may be selected to be cyclic-repeated in a firstcodebook according to the resource index with being repeated by apredetermined unit. The predetermined unit may be determined inconsideration of the spatial multiplexing rate.

The precoding matrix may be selected from a part of the first codebook.Or, the precoding matrix is selected from a second codebook comprising apart of the first codebook.

The precoding matrix may be selected from the first codebook on a basisof feedback information received from a reception end. And the feedbackinformation may include a precoding matrix index(PMI) associated withthe codebook.

It is to be understood that both the foregoing general description andthe following detailed description of the present invention areexemplary and explanatory and are intended to provide furtherexplanation of the invention as claimed.

[Advantageous Effects]

The present invention provides a phase-shift-based precoding techniquefor solving the problems of conventional CDD, PSD, and precodingmethods, resulting in the implementation of effective communication.Specifically, the phase-shift-based precoding technique is generalizedor extended, the design of a transceiver is simplified or thecommunication efficiency increases.

DESCRIPTION OF DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention, illustrate embodiments of the inventionand together with the description serve to explain the principle of theinvention.

In the drawings:

FIG. 1 is a block diagram illustrating an OFDM system equipped withmultiple transmission/reception (Tx/Rx) antennas;

FIG. 2 is a block diagram illustrating a transmission end of a MIMOsystem based on a conventional Cyclic Delay Diversity (CDD) scheme;

FIG. 3 is a block diagram illustrating a transmission end of a MIMOsystem based on a conventional phase shift diversity (PSD) scheme;

FIG. 4 is a block diagram illustrating a transceiver of a MIMO systembased on a conventional precoding scheme;

FIG. 5 is a block diagram illustrating the principal components of atransceiver for performing a phase-shift-based precoding schemeaccording to the present invention;

FIG. 6 graphically shows two applications of the phase-shift-basedprecoding or a phase shift diversity according to the present invention;

FIG. 7 is a block diagram illustrating a SCW OFDM transmitter based on aphase-shift-based precoding scheme according to the present invention;and

FIG. 8 is a block diagram illustrating a MCW OFDM transmitter accordingto the present invention.

BEST MODE

Reference will now be made in detail to the preferred embodiments of thepresent invention, examples of which are illustrated in the accompanyingdrawings. Wherever possible, the same reference numbers will be usedthroughout the drawings to refer to the same or like parts.

Prior to describing the present invention, it should be noted that mostterms disclosed in the present invention correspond to general termswell known in the art, but some terms have been selected by theapplicant as necessary and will hereinafter be disclosed in thefollowing description of the present invention. Therefore, it ispreferable that the terms defined by the applicant be understood on thebasis of their meanings in the present invention.

For the convenience of description and better understanding of thepresent invention, general structures and devices well known in the artwill be omitted or be denoted by a block diagram or a flow chart.Wherever possible, the same reference numbers will be used throughoutthe drawings to refer to the same or like parts.

First Embodiment

Phase-Shift-Based Precoding Matrix

FIG. 5 is a block diagram illustrating the principal components of atransceiver for performing a phase-shift-based precoding schemeaccording to the present invention.

The phase-shift-based precoding scheme multiplies sequences havingdifferent phases by all streams, and transmits the multiplied streamsvia all antennas. Generally, from the viewpoint of a receiver, if aphase sequence is generated with a small cyclic delay value, a channelmay have a frequency selectivity, and the size of the channel becomeslarger or smaller according to parts of a frequency domain.

As can be seen from FIG. 5, a transmitter allocates a user equipment(UE) to a specific part of a frequency band fluctuating with arelatively-small cyclic delay value, so that it acquires a schedulinggain from the specific part in which a frequency increases to implementa stable channel status. In this case, in order to apply a cyclic delayvalue regularly increasing or decreasing to individual antennas, thetransmitter uses the phase-shift-based precoding matrix.

The phase-shift-based precoding matrix (P) can be represented by thefollowing equation 1:

$\begin{matrix}{P_{N_{t} \times R}^{k} = \begin{pmatrix}w_{1,1}^{k} & w_{1,2}^{k} & \ldots & w_{1,R}^{k} \\w_{2,1}^{k} & w_{2,2}^{k} & \ldots & w_{2,R}^{k} \\\vdots & \vdots & ⋰ & \vdots \\w_{N_{t},1}^{k} & w_{N_{t},2}^{k} & \ldots & w_{N_{t},R}^{k}\end{pmatrix}} & \lbrack {{Equation}\mspace{20mu} 1} \rbrack\end{matrix}$

where k is a sub-carrier index or an index of a specific frequency band(k=1, 2, 3, 4, . . . ) or (k=0, 1, 2, 3, . . . ), θ_(i) (i=1, 2, 3, 4),w_(i,j) ^(k) (i=1, . . . , N_(t), j=1, . . . R) is a complex weightdecided by “k”, N_(t) is the number of Tx antennas, and R is a spatialmultiplexing rate.

In this case, the complex weight may have different values according toeither an OFDM symbol multiplied by antennas or a correspondingsub-carrier index. The complex weight may be determined by at least oneof a channel status and the presence or absence of feedback information.

In the meantime, it is preferable that the phase shift based precodingmatrix (P) of Equation 1 be configured in the form of a unitary matrixto reduce a loss of channel capacity in a MIMO system In this case, inorder to determine a constituent condition of the unitary matrix, achannel capacity of a MIMO open-loop system can be represented byEquation 2:

$\begin{matrix}{{C_{u}(H)} = {\log_{2}( {\det ( {I_{N_{t}} + {\frac{SNR}{N_{t}}{HH}^{H}}} )} )}} & \lbrack {{Equation}\mspace{20mu} 2} \rbrack\end{matrix}$

Where H is a (N_(r)×N_(t))-sized MIMO channel matrix, and N_(r) is thenumber of Rx antennas. If the phase-shift-based precoding matrix P isapplied to Equation 2, the following equation 3 is made:

$\begin{matrix}{C_{precoding} = {\log_{2}( {\det ( {I_{N_{t}} + {\frac{SNR}{N_{t}}{HPP}^{H}H^{H}}} )} )}} & \lbrack {{Equation}\mspace{20mu} 3} \rbrack\end{matrix}$

As can be seen from Equation 3, in order to prevent the channel capacityfrom being damaged, PP^(H) must be an identity matrix, so that thephase-shift-based precoding matrix P must satisfy the following equation4:

PP^(H)=I_(N)   [Equation 4]

Where I_(N) is n×n identity matrix.

In order to configure the phase-shift-based precoding matrix P in theform of a unitary matrix, the following two conditions must besimultaneously satisfied, i.e., a power limitation condition and anorthogonal limitation condition. The power limitation condition allowsthe size of each column of a matrix to be “1”, and can be represented bythe following equation 5:

$\begin{matrix}{{{{{w_{1,1}^{k}}^{2} + {w_{2,1}^{k}}^{2} + \ldots + {w_{N_{t},1}^{k}}^{2}} = 1},{{{w_{2,1}^{k}}^{2} + {w_{2,2}^{k}}^{2} + \ldots + {w_{N_{t},2}^{k}}^{2}} = 1},\vdots}{{{w_{1,R}^{k}}^{2} + {w_{2,R}^{k}}^{2} + \ldots + {w_{N_{t},R}^{k}}^{2}} = 1}} & \lbrack {{Equation}\mspace{20mu} 5} \rbrack\end{matrix}$

The orthogonal limitation condition allows individual columns to haveorthogonality there between, and can be represented by the followingequation 6:

$\begin{matrix}{{{{{w_{1,1}^{k^{*}}w_{1,2}^{k}} + {w_{2,1}^{k^{*}}w_{2,2}^{k}} + \ldots + {w_{N_{t},1}^{k^{*}}w_{N_{t},2}^{k}}} = 0},{{{w_{1,1}^{k^{*}}w_{1,3}^{k}} + {w_{2,1}^{k^{*}}w_{2,3}^{k}} + \ldots + {w_{N_{t},1}^{k^{*}}w_{N_{t},3}^{k}}} = 0},\vdots}{{{{w_{1,1}^{k^{*}}w_{1,R}^{k}} + {w_{2,1}^{k^{*}}w_{2,R}^{k}} + \ldots + {w_{N_{t},1}^{k^{*}}w_{N_{t},R}^{k}}} = 0},}} & \lbrack {{Equation}\mspace{20mu} 6} \rbrack\end{matrix}$

Next, a generalized equation of (2×2)-sized phase-shift-based precodingmatrix and an equation for satisfying the above-mentioned two conditionswill hereinafter be described in detail.

The following equation 7 shows a phase-shift-based precoding matrixwhich has a spatial multiplexing rate of 2 under 2 Tx antennas:

$\begin{matrix}{P_{2 \times 2}^{k} = \begin{pmatrix}{\alpha_{1}^{j\; k\; \theta_{1}}} & {\beta_{1}^{j\; k\; \theta_{2}}} \\{\beta_{2}^{j\; k\; \theta_{3}}} & {\alpha_{2}^{j\; k\; \theta_{4}}}\end{pmatrix}} & \lbrack {{Equation}\mspace{20mu} 7} \rbrack\end{matrix}$

where α_(i) and β_(i) (i=1, 2) have a real number, θ_(i) (i=1, 2, 3, 4)is a phase value, and k is a sub-carrier index of an OFDM symbol. Inorder to configure the above-mentioned precoding matrix in the form of aunitary matrix, the power limitation condition of the following equation8 and the orthogonal limitation condition of the following equation 9must be satisfied:

$\begin{matrix}{{{{{\alpha_{1}^{j\; k\; \theta_{1}}}}^{2} + {{\beta_{2}^{j\; k\; \theta_{3}}}}^{2}} = 1},{{{{\alpha_{2}^{j\; k\; \theta_{4}}}}^{2} + {{\beta_{1}^{j\; k\; \theta_{2}}}}^{2}} = 1}} & \lbrack {{Equation}\mspace{20mu} 8} \rbrack \\{{{( {\alpha_{1}^{j\; k\; \theta_{1}}} )^{*}\beta_{1}^{j\; k\; \theta_{2}}} + {( {\beta_{2}^{j\; k\; \theta_{3}}} )^{*}\alpha_{2}^{j\; k\; \theta_{4}}}} = 0} & \lbrack {{Equation}\mspace{20mu} 9} \rbrack\end{matrix}$

where “*” is a conjugate complex number.

An example of the (2×2)-sized phase-shift-based precoding matrixsatisfying Equations 8 and 9 is represented by the following equation10:

$\begin{matrix}{P_{2 \times 2}^{k} = {\frac{1}{\sqrt{2}}\begin{pmatrix}1 & ^{j\; k\; \theta_{2}} \\^{j\; k\; \theta_{3}} & 1\end{pmatrix}}} & \lbrack {{Equation}\mspace{20mu} 10} \rbrack\end{matrix}$

where the relationship between θ₂ and θ₃ is represented by the followingequation 11:

kθ ₃ =kθ ₂+π  [Equation 11]

At least one precoding matrix may be configured in the form of acodebook, so that the codebook-formatted precoding matrix may be storedin a memory of a transmission- or reception-end. The codebook mayinclude a variety of precoding matrixes created by different finite θ₂values.

In this case, “θ₂” may be properly established by a channel status andthe presence or absence of feedback information. If the feedbackinformation is used, “θ₂” is set to a low value. If the feedbackinformation is not in use, “θ₂” is set to a high value. As a result, ahigh frequency diversity gain is acquired.

In the meantime, a frequency diversity gain or frequency scheduling gainmay be acquired according to the size of a delay sample applied to thephase-shift-based precoding.

FIG. 6 graphically shows two applications of the phase-shift-basedprecoding or a phase shift diversity according to the present invention.

As can be seen from FIG. 6, if a delay sample (or a cyclic delay) of alarge value is used, a frequency-selective period becomes shorter, sothat a frequency selectivity increases and a channel code may acquire afrequency diversity gain. So, it is preferable that the large-valuedelay sample be used for an open-loop system in which the reliability offeedback information deteriorates due to an abrupt channel variation intime.

If a delay sample of a small value is used, a first part in which thechannel size becomes larger and a second part in which the channel sizebecomes smaller occur in a frequency-selective channel changed from aflat-fading channel. Therefore, the channel size becomes larger in apredetermined sub-carrier area of the OFDM signal, and becomes smallerin the other sub-carrier area.

In this case, if at an Orthogonal Frequency Division Multiple Access(OFDMA) system accommodating several users an objective signal istransmitted via a larger-channel-sized frequency band for each user, aSignal-to-Noise Ratio (SNR) can be increased. And, the each user mayhave different larger-channel-sized frequency bands very often, so thatthe system can acquire a multi-user diversity scheduling gain. From theviewpoint of a reception end, it can transmit Channel Quality Indicator(CQI) information of only a sub-carrier area to allocate resource asfeedback information, so that an amount of the feedback information isrelatively reduced.

A delay sample (or cyclic delay) for the phase-shift-based precoding maybe predetermined in a transceiver, or may be fed back from a receiver toa transmitter.

Also, the spatial multiplexing rate R may also be predetermined in thetransceiver. However, a receiver periodically recognizes a channelstatus, calculates the spatial multiplexing rate, and feeds back thecalculated spatial multiplexing rate to a transmitter. Otherwise, thetransmitter may calculate or change the spatial multiplexing rate usingchannel information fed back from the receiver.

Second Embodiment

Generalized Phase Shift Diversity Matrix

In the case of being used in a system in which the number of antennas isN_(t) (N_(t) is a natural number higher than 2) and a spatialmultiplexing rate is R, the above-mentioned phase-shift-based precodingmatrix can be represented by the following equation 12:

$\begin{matrix}\begin{matrix}{{GPSD}_{N_{t} \times R}^{k} = \begin{pmatrix}w_{1,1}^{k} & w_{1,2}^{k} & \ldots & w_{1,R}^{k} \\w_{2,1}^{k} & w_{2,2}^{k} & \ldots & w_{2,R}^{k} \\\vdots & \vdots & ⋰ & \vdots \\w_{N_{t},1}^{k} & w_{N_{t},2}^{k} & \ldots & w_{N_{t},R}^{k}\end{pmatrix}} \\{= {\begin{pmatrix}^{j\; \theta_{1}k} & 0 & \ldots & 0 \\0 & ^{j\; \theta_{2}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & 0 \\0 & 0 & 0 & ^{j\; \theta_{N_{t}}k}\end{pmatrix}( U_{N_{t} \times R}^{k} )}}\end{matrix} & \lbrack {{Equation}\mspace{20mu} 12} \rbrack\end{matrix}$

Equation 12 may be considered to be a generalized format of theconventional phase shift diversity scheme, so that the MIMO scheme shownin Equation 12 will hereinafter be referred to as a Generalized PhaseShift Diversity (GPSD) scheme.

In Equation 12,

GPSD_(N_(t) × R)^(k)

is a GPSD matrix of a k-th sub-carrier of a MIMO-OFDM signal which hasN_(t) Tx antennas and a spatial multiplexing rate of R. And, UN_(t)×R isa unitary matrix (i.e., a second matrix) satisfying

U_(N_(t) × R)^(H) × U_(N_(t) × R) = _(R × R),

and is adapted to minimize an interference between sub-carrier symbolscorresponding to individual antennas. Specifically, in order to maintaina diagonal matrix (i.e., a first matrix) for a phase shift without anychange, it is preferable that UN_(t)×R may satisfy the condition of theunitary matrix. In Equation 12, a phase angle θ_(i) (i=1, . . . , N_(t))of a frequency domain and a delay time τ_(i) (i=1, . . . , N_(t)) of atime domain have a predetermined relationship, which is represented bythe following equation 13:

$\begin{matrix}{\theta_{i} = {{- 2}{{\pi/N_{fft}} \cdot \tau_{i}}}} & \lbrack {{Equation}\mspace{20mu} 13} \rbrack\end{matrix}$

where N_(fft) is the number of sub-carriers of an OFDM signal.

A modified example of Equation 12 is shown in the following equation 14,so that the GPSD matrix can be calculated by Equation 14:

$\begin{matrix}\begin{matrix}{{GPSD}_{N_{t} \times R}^{k} = \begin{pmatrix}w_{1,1}^{k} & w_{1,2}^{k} & \ldots & w_{1,R}^{k} \\w_{2,1}^{k} & w_{2,2}^{k} & \ldots & w_{2,R}^{k} \\\vdots & \vdots & ⋰ & \vdots \\w_{N_{t},1}^{k} & w_{N_{t},2}^{k} & \ldots & w_{N_{t},R}^{k}\end{pmatrix}} \\{= {( U_{N_{t} \times R}^{k} )\begin{pmatrix}^{j\; \theta_{1}k} & 0 & \ldots & 0 \\0 & ^{j\; \theta_{2}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & 0 \\0 & 0 & 0 & ^{j\; \theta_{R}k}\end{pmatrix}}}\end{matrix} & \lbrack {{Equation}\mspace{20mu} 14} \rbrack\end{matrix}$

If the GPSD matrix is made by Equation 14, symbols of each data stream(or OFDM sub-carrier) are shifted by the same phase, so that the GPSDmatrix can be easily configured. In other words, the GPSD matrix ofEquation 14 has columns having the same phase whereas the GPSD matrix ofEquation 12 has rows having the same phase, so that the individualsub-carrier symbols are shifted by the same phase. If Equation 14 isextended, the GPSD matrix can be calculated by the following equation15:

$\begin{matrix}{{GPSD}_{N_{t} \times R}^{k} = {\begin{pmatrix}w_{1,1}^{k} & w_{1,2}^{k} & \ldots & w_{1,R}^{k} \\w_{2,1}^{k} & w_{2,2}^{k} & \ldots & w_{2,R}^{k} \\\vdots & \vdots & ⋰ & \vdots \\w_{N_{t},1}^{k} & w_{N_{t},2}^{k} & \ldots & w_{N_{t},R}^{k}\end{pmatrix} = {\begin{pmatrix}^{j\; \theta_{1}k} & 0 & \ldots & 0 \\0 & ^{j\; \theta_{2}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & 0 \\0 & 0 & 0 & ^{j\; \theta_{N_{t}}k}\end{pmatrix}( U_{N_{t} \times R}^{k} )\begin{pmatrix}^{j\; \theta_{1}^{\prime}k} & 0 & \ldots & 0 \\0 & ^{j\; \theta_{2}^{\prime}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & 0 \\0 & 0 & 0 & ^{j\; \theta_{R}^{\prime}k}\end{pmatrix}}}} & \lbrack {{Equation}\mspace{20mu} 15} \rbrack\end{matrix}$

As can be seen from Equation 15, rows and columns of the GPSD matrixhave independent phases, so that a variety of frequency diversity gainscan be acquired.

As an example of Equation 12, 14 or 15, a GPSD matrix equation of asystem which uses two Tx antennas and a 1-bit codebook can berepresented by the following equation 16:

$\begin{matrix}{{{GPSD}_{2 \times 2}^{k} = \begin{pmatrix}\alpha & \beta \\\beta & {- \alpha}\end{pmatrix}},{{\alpha^{2} + \beta^{2}} = 1}} & \lbrack {{Equation}\mspace{20mu} 16} \rbrack\end{matrix}$

In Equation 16, if “α” is decided, “β” is easily decided. So, the valueof “α” may be fixed to two proper values, and information associatedwith the value of “α” may be fed back to a codebook index as necessary.For example, two conditions may be prescribed between a transmitter anda receiver, i.e., one condition in which “α” is set to “0.2” if afeedback index is “0”, and the other condition in which “α” is set to“0.8” if a feedback index is “1”.

a predetermined precoding matrix for acquiring a SNR gain may be used asan example of the unitary matrix UN_(t)×R in Equation 12, 14, or 15. AWalsh Hadamard matrix or a DFT matrix may be used as the above-mentionedprecoding matrix. If the Walsh Hadamard matrix is used, an example ofthe GPSD matrix of Equation 12 can be represented by the followingequation 17:

$\begin{matrix}{{GPSD}_{4 \times 4}^{k} = {\frac{1}{\sqrt{4}}\begin{pmatrix}^{{j\theta}_{1}k} & 0 & 0 & 0 \\0 & ^{{j\theta}_{2}k} & 0 & 0 \\0 & 0 & ^{{j\theta}_{3}k} & 0 \\0 & 0 & 0 & ^{{j\theta}_{4}k}\end{pmatrix}\begin{pmatrix}1 & 1 & 1 & 1 \\1 & {- 1} & 1 & {- 1} \\1 & 1 & {- 1} & {- 1} \\1 & {- 1} & {- 1} & 1\end{pmatrix}}} & \lbrack {{Equation}\mspace{20mu} 17} \rbrack\end{matrix}$

Equation 17 is made on the assumption that a system has 4 Tx antennasand a spatial multiplexing rate of 4. In this case, the second matrix isproperly reconstructed, so that a specific Tx antenna is selected (i.e.,antenna selection) or the spatial multiplexing rate may be tuned (i.e.,rank adaptation).

In the meantime, the unitary matrix UN_(t)×R of Equation 12, 14 or 15may be configured in the form of a codebook, so that thecodebook-formatted unitary matrix is stored in a transmission orreception end. In this case, the transmission end receives codebookindex information from the reception end, selects a precoding matrix ofa corresponding index from its own codebook, and configures aphase-shift-based precoding matrix using Equations 12, 14, or 15.

If a (2×2)- or (4×4)-sized Walsh code is used as the unitary matrixUN_(t)×R of Equation 12, 14, or 15, an example of the GPSD matrix isacquired, as represented by the following Tables 2 and 3:

TABLE 2 2 Tx Rate 1 Rate 2 $\frac{1}{\sqrt{2}}\begin{bmatrix}1 \\e^{j\; \theta_{1}k}\end{bmatrix}$ $\frac{1}{\sqrt{2}}\begin{bmatrix}1 & 1 \\e^{j\; \theta_{1}k} & {- e^{j\; \theta_{1}k}}\end{bmatrix}$

TABLE 3 4 Tx Rate 1 Rate 2 Rate 4 $\frac{1}{2}\begin{bmatrix}1 \\e^{j\; \theta_{1}k} \\e^{j\; \theta_{2}k} \\e^{j\; \theta_{3}k}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 1 \\e^{j\; \theta_{1}k} & {- e^{j\; \theta_{1}k}} \\e^{j\; \theta_{2}k} & {- e^{j\; \theta_{2}k}} \\e^{j\; \theta_{3}k} & {- e^{j\; \theta_{3}k}}\end{bmatrix}$ $\frac{1}{2}\begin{bmatrix}1 & 1 & 1 & 1 \\e^{j\; \theta_{1}k} & {- e^{j\; \theta_{1}k}} & e^{j\; \theta_{1}k} & {- e^{j\; \theta_{1}k}} \\e^{j\; \theta_{2}k} & e^{j\; \theta_{2}k} & {- e^{j\; \theta_{2}k}} & {- e^{j\; \theta_{2}k}} \\e^{j\; \theta_{3}k} & {- e^{j\; \theta_{3}k}} & {- e^{j\; \theta_{3}k}} & e^{j\; \theta_{3}k}\end{bmatrix}$

Third Embodiment

Time-Variant Generalized Phase Shift Diversity

In the GPSD matrix of Equation 12, 14, or 15, a phase angle (θ_(i)) of adiagonal matrix and/or a unitary matrix (U) may be changed in time. Forexample, a time-variant GPSD of Equation 12 can be represented by thefollowing equation 18:

$\begin{matrix}{{{GPSD}_{N_{t} \times R}^{k}(t)} = {\begin{pmatrix}^{j\; {\theta_{1}{(t)}}k} & 0 & \ldots & 0 \\0 & ^{j\; {\theta_{2}{(t)}}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & 0 \\0 & 0 & 0 & ^{j\; {\theta_{N_{t}}{(t)}}k}\end{pmatrix}( {U_{N_{t} \times R}(t)} )}} & \lbrack {{Equation}\mspace{20mu} 18} \rbrack\end{matrix}$

where

GPSD_(N_(t) × R)^(k)(t)

is a GPSD matrix of a k-th sub-carrier of a MIMO-OFDM signal which hasN_(t) Tx antennas and a spatial multiplexing rate of R at a specifictime (t) UN_(t)×R(t) is a unitary matrix (i.e., a fourth matrix)satisfying

U_(N_(t) × R)^(H) × U_(N_(t) × R) = _(R × R),

and is adapted to minimize an interference between sub-carrier symbolscorresponding to individual antennas.

Specifically, in order to maintain characteristics of the unitary matrixof a diagonal matrix (i.e., third matrix) for a phase shift without anychange, it is preferable that UN_(t)×R(t) may satisfy the condition ofthe unitary matrix. In Equation 18, a phase angle θ_(i)(t) (i=1, . . . ,N_(t)) and a delay time τ_(i)(t) (i=1, . . . , N_(t)) have apredetermined relationship, which is represented by the followingequation 19:

$\begin{matrix}{{\theta_{i}(t)} = {{- 2}{{\pi/N_{fft}} \cdot {\tau_{i}(t)}}}} & \lbrack {{Equation}\mspace{20mu} 19} \rbrack\end{matrix}$

where N_(fft) is the number of sub-carriers of an OFDM signal.

As can be seen from Equations 18 and 19, a time delay sample value and aunitary matrix may be changed in time. In this case, a unitary of thetime may be set to an OFDM symbol or a predetermined-unitary time.

If a unitary matrix for acquiring a time-variant GPSD is represented bya GPSD matrix based on the (2×2)-sized Walsh code, the following GPSDmatrix can be made as shown in the following Table 4:

TABLE 4 2 Tx Rate 1 Rate 2 $\begin{bmatrix}1 \\e^{j\; {\theta_{1}{(t)}}k}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 1 \\e^{j\; {\theta_{1}{(t)}}k} & {- e^{j\; {\theta_{1}{(t)}}k}}\end{bmatrix}\quad$

If a unitary matrix for acquiring a time-variant GPSD is represented bya GPSD matrix based on the (4×4)-sized Walsh code, the following GPSDmatrix can be made as shown in the following Table 5:

TABLE 5 4 Tx Rate 1 Rate 2 Rate 4 $\begin{bmatrix}1 \\e^{j\; {\theta_{1}{(t)}}k} \\e^{j\; {\theta_{2}{(t)}}k} \\e^{j\; {\theta_{3}{(t)}}k}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 1 \\e^{j\; {\theta_{1}{(t)}}k} & {- e^{j\; {\theta_{1}{(t)}}k}} \\e^{j\; {\theta_{2}{(t)}}k} & e^{j\; {\theta_{2}{(t)}}k} \\e^{j\; {\theta_{3}{(t)}}k} & {- e^{j\; {\theta_{3}{(t)}}k}}\end{bmatrix}\quad$ $\begin{bmatrix}1 & 1 & 1 & 1 \\e^{j\; {\theta_{1}{(t)}}k} & {- e^{j\; {\theta_{1}{(t)}}k}} & e^{j\; {\theta_{1}{(t)}}k} & {- e^{j\; {\theta_{1}{(t)}}k}} \\e^{j\; {\theta_{2}{(t)}}k} & e^{j\; {\theta_{2}{(t)}}k} & {- e^{j\; {\theta_{2}{(t)}}k}} & {- e^{j\; {\theta_{2}{(t)}}k}} \\e^{j\; {\theta_{3}{(t)}}k} & {- e^{j\; {\theta_{3}{(t)}}k}} & {- e^{j\; {\theta_{3}{(t)}}k}} & e^{j\; {\theta_{3}{(t)}}k}\end{bmatrix}\quad$

Although the above-mentioned third embodiment has disclosed thetime-variant GPSD matrix associated with Equation 12, it should be notedthat the time-variant GPSD matrix can also be applied to the diagonalmatrix and unitary matrix of Equations 14 and 15. Therefore, althoughthe following embodiments will be described with reference to Equation12, it is obvious to those skilled in the art that the scope of thefollowing embodiments are not limited to Equation 12 and can also beapplied to Equations 14 and 15.

Fourth Embodiment

Extension of Generalized Phase Shift Diversity

If a third matrix corresponding to a precoding matrix is added to theGPSD matrix composed of both a diagonal matrix and a unitary matrix, anextended GPSD matrix can be made as shown in the following equation 20:

$\begin{matrix}{{GPSD}_{N_{t} \times R}^{k} = {( {\mathbb{P}}_{N_{t} \times R} )\begin{pmatrix}^{j\; \theta_{1}k} & 0 & \ldots & 0 \\0 & ^{j\; \theta_{2}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & 0 \\0 & 0 & 0 & ^{j\; \theta_{R}k}\end{pmatrix}( _{R \times R} )}} & \lbrack {{Equation}\mspace{20mu} 20} \rbrack\end{matrix}$

Compared with Equation 12, the extended GPSD matrix of Equation 20further includes a (N_(t)×R)-sized precoding matrix (P) located before adiagonal matrix. Therefore, the size of the diagonal matrix is changedto a (R×R)-size.

The added precoding matrix PN_(t)×R may be differently assigned to aspecific frequency band or a specific sub-carrier symbol. Preferably, inthe case of an open-loop system, the added precoding matrix PN_(t)×R maybe set to a fixed matrix. By the addition of the precoding matrixPN_(t)×R, an optimum SNR gain can be acquired.

A transmission end or reception end may have a codebook equipped with aplurality of precoding matrixes (P).

In the meantime, in the extended GPSD matrix, at least one of theprecoding matrix (P), the phase angle (θ) of the diagonal matrix, andthe unitary matrix (U) may be changed in time. For this purpose, if anindex of the next precoding matrix P is fed back in units of apredetermined time or a predetermined sub-carrier, a specific precodingmatrix P corresponding to the index may be selected from a predeterminedcodebook.

The extended GPSD matrix according to the fourth embodiment can berepresented by the following equation 21:

$\begin{matrix}{{{GPSD}_{N_{t} \times R}^{k}(t)} = {( {{\mathbb{P}}_{N_{t} \times R}(t)} )\begin{pmatrix}^{j\; {\theta_{1}{(t)}}k} & 0 & \ldots & 0 \\0 & ^{j\; {\theta_{2}{(t)}}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & 0 \\0 & 0 & 0 & ^{j\; {\theta_{R}{(t)}}k}\end{pmatrix}( {_{R \times R}(t)} )}} & \lbrack {{Equation}\mspace{20mu} 21} \rbrack\end{matrix}$

As an example of the extended GPSD matrix, a matrix equation of a MIMOsystem which includes two or four Tx antennas is shown in the followingequations 22 and 23:

$\begin{matrix}{\mspace{79mu} {{{GPSD}_{2 \times 2}^{k}(t)} = {( {{\mathbb{P}}_{2 \times 2}(t)} )\begin{pmatrix}1 & 0 \\0 & ^{{{j\theta}{(t)}}k}\end{pmatrix}( {DFT}_{2 \times 2} )}}} & \lbrack {{Equation}\mspace{20mu} 22} \rbrack \\{{{GPSD}_{4 \times R}^{k}(t)} = {( {{\mathbb{P}}_{4 \times R}(t)} )\begin{pmatrix}1 & 0 & \ldots & 0 \\0 & ^{{{j\theta}{(t)}}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & \vdots \\0 & 0 & \ldots & ^{{j{({R - 1})}}{\theta {(t)}}k}\end{pmatrix}( {DFT}_{4 \times R} )}} & \lbrack {{Equation}\mspace{20mu} 23} \rbrack\end{matrix}$

In Equations 22 and 23, although a DFT matrix is used as a unitarymatrix, the scope of the present invention is not limited to the DFTmatrix, and can also be applied to other matrixes capable of satisfyinga given unitary condition such as a Walsh Hadamard code.

As another example of the extended GPSD matrix, a matrix equation of aMIMO system which includes four Tx antennas is shown in the followingequation 24:

$\begin{matrix}{{{GPSD}_{N_{t} \times R}^{k}(t)} = {\underset{\underset{D\; 1}{}}{\begin{pmatrix}^{{{j\theta}_{1}^{\prime}{(t)}}k} & 0 & \ldots & 0 \\0 & ^{{{j\theta}_{2}^{\prime}{(t)}}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & \vdots \\0 & 0 & \ldots & ^{{{j\theta}_{N_{t}}^{\prime}{(t)}}k}\end{pmatrix}}( {P_{N_{t} \times R}(t)} )\underset{\underset{D\; 2}{}}{\begin{pmatrix}^{{{j\theta}_{1}{(t)}}k} & 0 & \ldots & 0 \\0 & ^{{{j\theta}_{2}{(t)}}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & \vdots \\0 & 0 & \ldots & ^{{{j\theta}_{R}{(t)}}k}\end{pmatrix}}( U_{R \times R} )}} & \lbrack {{Equation}\mspace{20mu} 24} \rbrack\end{matrix}$

Compared with Equation 12, the extended GPSD matrix of Equation 24further includes a (N_(t)×N_(t))-sized diagonal matrix (D1) and a(N_(t)×R)-sized precoding matrix (P), which are located before adiagonal matrix (D2). Therefore, the size of the diagonal matrix (D2) ischanged to a (R×R)-size.

The added precoding matrix PN_(t)×R may be differently assigned to aspecific frequency band or a specific sub-carrier symbol. Preferably, inthe case of an open-loop system, the added precoding matrix PN_(t)×R maybe set to a fixed matrix. By the addition of the precoding matrixPN_(t)×R, an optimum SNR gain can be acquired.

Preferably, a transmission end or reception end may have a codebookequipped with a plurality of precoding matrixes (P).

In this case, by the diagonal matrixes D1 and D2, a phase angle can beshifted in two ways in a single system. For example, if a low-valuephase shift is used by the diagonal matrix D1, a multi-user diversityscheduling gain can be acquired. If a high-value phase shift is used bythe diagonal matrix D2, a frequency diversity gain can be acquired. Thediagonal matrix D1 is adapted to increase a system performance, and theother diagonal matrix D2 is adapted to average a channel betweenstreams.

And, a high-value phase shift is used by the diagonal matrix D1, so thata frequency diversity gain can increase. A high-value phase shiftdiversity is used by the diagonal matrix D2, a channel between streamscan be averaged. This gain can be acquired from Equation 21.

In this case, the matrix P of Equation 21 must be changed on the basisof a sub-carrier unit or frequency resource unit, and be then usedwithout feedback information. This modified format can be represented bythe following equation 25:

$\begin{matrix}{{{GPSD}_{N_{t} \times R}^{k}(t)} = {\begin{pmatrix}^{{{j\theta}_{1}{(t)}}k} & 0 & \ldots & 0 \\0 & ^{{{j\theta}_{2}{(t)}}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & \vdots \\0 & 0 & \ldots & ^{{{j\theta}_{R}{(t)}}k}\end{pmatrix}( U_{R \times R} )}} & \lbrack {{Equation}\mspace{20mu} 25} \rbrack\end{matrix}$

In Equation 25, P_(N) _(t) _(×R) ^(k)(t) is indicative of a specificcase, in which individual resource indexes (k) use different precodingmatrixes. Thereby, a frequency diversity gain increases by usingdifferent precoding matrixes per resource indexes (k), and a channelbetween streams is averaged by using a diagonal matrix and an identitymatrix (U).

Fifth Embodiment

Codebook Subset Limitation Scheme

The codebook subset limitation scheme is to be restricted to use someparts of a codebook. Provided that the number of all precoding matrixesof the codebook is N_(c), only N_(restrict) precoding matrixes areusable according to the codebook subset limitation scheme. The codebooksubset limitation scheme may be used to reduce a multi-cell interferenceor system complexity. In this case, a predetermined condition denoted byN_(restrict)≦N_(c) must be satisfied.

For example, Provided that the number of all precoding matrixes of thecodebook is N_(c)=6, a codebook P_(n) _(t) _(×R) of all sets and aspecific codebook _(N) _(t) _(×R) ^(restrict) for allowing only 4precoding matrixes from among 6 precoding matrixes to be used can berepresented by the following equation 26:

P _(N) _(t) _(×R) ={P _(N) _(t) _(×R) ⁰ , P _(N) _(t) _(×R) ¹ , P _(N)_(t) _(×R) ² , P _(N) _(t) _(×R) ³ , O _(N) _(t) _(×R) ⁴ , P _(N) _(t)_(×R) ⁵},

P _(N) _(t) _(×R) ^(restrict) ={P _(N) _(t) _(×R) ⁰ , P _(N) _(t) _(×R)² , P _(N) _(t) _(×R) ³ , P _(N) _(t) _(×R) ⁵ }=W _(N) _(t) _(×R) ={W_(N) _(t) _(×r) ⁰ , W _(N) _(t) _(×R) ¹ , W _(N) _(t) _(×R) ¹ , W _(N)_(t) _(×R) ² , W _(N) _(t) _(×R)}  [Equation 26]

In Equation 26, W_(N) _(t) _(×R) is an equivalent codebook of thecodebook P_(N) _(t) _(×R) ^(restrict).

Sixth Embodiment

Precoding Matrixes Cyclic Repetition Scheme

For example, if a set of precoding matrixes determined during a Tx/Rxtime is pre-defined at a specific time, this case can be represented bythe following equation 27:

$\begin{matrix}{\mspace{79mu} {{P_{N_{t} \times R} = \{ {P_{N_{t} \times R}^{0},P_{N_{t} \times R}^{1},\ldots \mspace{11mu},P_{N_{t} \times R}^{N_{c} - 1}} \}}{{GPSD}_{N_{t} \times R}^{k} = {( P_{N_{t} \times R}^{k\; {mod}\; N_{t}} )\begin{pmatrix}^{{{j\theta}_{1}{(t)}}k} & 0 & \ldots & 0 \\0 & ^{{{j\theta}_{2}{(t)}}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & \vdots \\0 & 0 & \ldots & ^{{{j\theta}_{R}{(t)}}k}\end{pmatrix}( U_{R \times R} )}}}} & \lbrack {{Equation}\mspace{20mu} 27} \rbrack\end{matrix}$

In Equation 27, the set of precoding matrixes includes N_(c) precodingmatrixes.

Equation 27 can be simplified in the form of Equation 28:

P _(N) _(t) _(×R) ={P _(N) _(t) _(×R) ⁰ , P _(N) _(t) _(×R) ¹ , . . . ,P _(N) _(t) _(×R) ^(N) ^(c) ⁻¹}

GPSD_(N) _(t) _(×R) ^(l)=(P _(N) _(t) _(×r) ^(k mod N) ^(c) )Π_(R×R)^(l)   [Equation 28]

In Equation 27 and Equation 28, P_(N) _(t) _(×R) ^(k mod N) ^(c) isindicative of a precoding matrix cyclic-repeated according to a subcarrier index or a resource index k among N_(c) precoding matrixesincluded in a codebook P_(N) _(t) _(×R).

In Equation 28, Π_(R×R) ^(k) is adapted to mix data streams, and may becalled a rotation matrix. As can be seen from Equation 28, Π_(R×R) ^(k)may be selected according to a spatial multiplexing rate (R). Π_(R×R)^(k) may also be easily represented by the following equation 29:

[Equation 29]

Spatial multiplexing Rate:2

$\Pi_{2 \times 2}^{k} = {\begin{pmatrix}0 & 1 \\1 & 0\end{pmatrix}^{k}\mspace{14mu} {or}\mspace{14mu} \begin{pmatrix}1 & 0 \\0 & ^{{j\theta}_{3}k}\end{pmatrix}{DFT}_{2 \times 2}}$

Spatial multiplexing Rate:3

$\Pi_{3 \times 3}^{k} = {\begin{pmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{pmatrix}^{k}\mspace{14mu} {or}\mspace{14mu} \begin{pmatrix}1 & 0 & 0 \\0 & ^{{j\theta}_{1}k} & 0 \\0 & 0 & ^{{j\theta}_{2}k}\end{pmatrix}{DFT}_{3 \times 3}}$

Spatial multiplexing Rate:4

$\Pi_{4 \times 4}^{k} = {\begin{pmatrix}0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1 \\1 & 0 & 0 & 0\end{pmatrix}^{k}\mspace{14mu} {or}\mspace{14mu} \begin{pmatrix}1 & 0 & 0 & 0 \\0 & ^{{j\theta}_{1}k} & 0 & 0 \\0 & 0 & ^{{j\theta}_{2}k} & 0 \\0 & 0 & \; & ^{{j\theta}_{3}k}\end{pmatrix}{DFT}_{4 \times 4}}$

In addition, in a codebook equipped with N_(c) precoding matrixes, if acodebook subset limitation scheme capable of using only a specific partof the codebook according to a Node-B or user equipment (UE) is appliedto the above-mentioned codebook, N_(c) precoding matrixes must bereduced to N_(restrict) precoding matrixes, and be then used.

Therefore, in the case of using the equivalent codebook W_(N) _(t)_(×R), Equation 28 can be represented by the following equation 30:

P _(N) _(t) _(×R) ^(restrict) ={P _(N) _(t) _(×R) ⁰ , P _(N) _(t) _(×R)² , P _(N) _(t) _(×R) ³ , P _(N) _(t) _(×R) ⁵ }=W _(N) _(t) _(×R) ={W_(N) _(t) _(×R) ¹ , W _(N) _(t) _(×R) ² , W _(N) _(t) _(×R) ³}

GPSD_(N) _(t) _(×R) ^(k) ={W _(N) _(t) _(×R) ^(k mod N) ^(restrict))Π_(R×R) ^(k)   [Equation 30]

where “k” is a sub-carrier index or a frequency-resource index. InEquation 30, N_(restrict) is 4. And in Equation 30, W_(N) _(t) _(×R)^(k mod N) ^(restrict) is indicative of a precoding matrixcyclic-repeated according to a sub carrier index or a resource index kamong N_(restrict) precoding matrixes included in a codebook P_(N) _(t)_(×R) ^(restrict) or W_(N) _(t) _(×R).

Sixth Embodiment

Precoding Matrixes Cyclic Repetition Scheme by a Predetermined Unit

And, Equation 28 can also be represented by the following equation 31according to a setup of frequency resources:

$\begin{matrix}{{P_{N_{t} \times R} = \{ {P_{N_{t} \times R}^{0},P_{N_{t} \times R}^{1},\ldots \mspace{11mu},P_{N_{t} \times R}^{N_{c} - 1}} \}}{{GPSD}_{N_{t} \times R}^{k} = {( P_{N_{t} \times R}^{{\lceil\frac{k}{v}\rceil}\mspace{11mu} {mod}\mspace{11mu} N_{c}} )\Pi_{R \times R}^{k}}}{{{or}\mspace{20mu} {GPSD}_{N_{t} \times R}^{k}} = {( P_{N_{t} \times R}^{{\lfloor\frac{k}{v}\rfloor}\mspace{11mu} {mod}\mspace{11mu} N_{c}} )\Pi_{R \times R}^{k}}}} & \lbrack {{Equation}\mspace{20mu} 31} \rbrack\end{matrix}$

In Equation 31, “k” may be a sub-carrier index or a virtual-resourceindex and GPSD_(N) _(t) _(×R) ^(k) can be selected among 2 ways inEquation 31 according to what started index k is.

In Equation 31, if “k” is the sub-carrier index, a precoding matrix isrepeated for v sub carriers and the precoding matrix is cyclic-repeatedaccording to a sub carrier index k among N_(c) precoding matrixesincluded in a codebook P_(N) _(t) _(×R).

Exemplary listings of precoding matrix index per sub carrier are asfollows:

[1122334455 1122334455 . . . ]

or [000111222333444 000111222333444 . . . ]

The first one represents the case of v=2, N_(c)=5 and k=1,2, . . . , K,and the second one represents the case of v=3, N_(c)=5, k=0,1, . . . ,K−1. In here, K is a number of resources in a sub-frame.

Equation 31 shows a specific case in which a precoding matrix isdifferently established in N_(c) precoding matrixes. The value of v maybe decided by considering a spatial multiplexing rate of the precodingmatrix. For example, the value of v may be denoted by v=R.

Also, in the case of using the codebook subset limitation scheme ofEquations 26, the precoding matrix may also be changed on the basis of apredetermined number of sub-carrier units or a predetermined number offrequency resource units. This format can be represented by thefollowing equation 32:

$\begin{matrix}{\begin{matrix}{P_{N_{t} \times R}^{restrict} = \{ {P_{N_{t} \times R}^{0},P_{N_{t} \times R}^{2},P_{N_{t} \times R}^{3}\mspace{11mu},P_{N_{t} \times R}^{5}} \}} \\{= W_{N_{t} \times R}} \\{= \{ {W_{N_{t} \times R}^{0},W_{N_{t} \times R}^{2},W_{N_{t} \times R}^{3}\mspace{11mu},W_{N_{t} \times R}^{5}} \}}\end{matrix}{{GPSD}_{N_{t} \times R}^{k} = {( W_{N_{t} \times R}^{{\lceil\frac{k}{v}\rceil}\mspace{11mu} {mod}\mspace{11mu} N_{restrict}} )\Pi_{R \times R}^{k}}}{or}{{GPSD}_{N_{t} \times R}^{k} = {( W_{N_{t} \times R}^{{\lfloor\frac{k}{v}\rfloor}\mspace{14mu} {mod}\mspace{11mu} N_{restrict}} )\Pi_{R \times R}^{k}}}} & \lbrack {{Equation}\mspace{20mu} 32} \rbrack\end{matrix}$

Compared with Equation 31, the precoding matrix of Equation 32 may alsobe changed by v units. Differently from Equation 31, the precodingmatrix of Equation 32 is changed in N_(restrict) (≦N_(c)) number ofprecoding matrixes.

In the meantime, frequency diversity gain could be changed according tothe number of cyclic-repeated precoding matrixes or the number ofprecoding matrixes included in the codebook. Therefore, in case that thecodebook subset limitation scheme and precoding matrixes cyclicrepetition scheme are adapted in together as represented in Equation 32,various schemes for determining the codebook subset are described asbelow.

Fifth Embodiment-1

According to Spatial Multiplexing Rate R

The codebook subset can be determined differently according to thespatial multiplexing rate R. For example, in case of a low spatialmultiplexing rate, the size of the codebook subset is determined to belarge, such that frequency diversity gain can be achieved up to themaximum. And in case of a high spatial multiplexing rate, the size ofthe codebook subset is determined to be small, such that the complexitycan be decreased with maintaining the performance.

In case of using codebook subset determined according to the spatialmultiplexing rate R, the example method can be represented by thefollowing equation 33:

$\begin{matrix}{{{W_{N_{t} \times 2} = \{ {W_{N_{t} \times R}^{0},W_{N_{t} \times R}^{1},W_{N_{t} \times R}^{2}\mspace{11mu},W_{N_{t} \times R}^{3}} \}},{N_{restrict}^{2} = 4}}{{W_{N_{t} \times 3} = \{ {W_{N_{t} \times R}^{0},W_{N_{t} \times R}^{1},W_{N_{t} \times R}^{2}}\; \}},{N_{restrict}^{3} = 3}}{{W_{N_{t} \times 4} = \{ W_{N_{t} \times R}^{0} \}},{N_{restrict}^{4} = 1}}{{GPSD}_{N_{t} \times R}^{k} = {( W_{N_{t} \times R}^{{\lceil\frac{k}{v}\rceil}\mspace{11mu} {mod}\mspace{11mu} N_{restrict}} )\Pi_{R \times R}^{k}}}{or}{{GPSD}_{N_{t} \times R}^{k} = {( W_{N_{t} \times R}^{{\lfloor\frac{k}{v}\rfloor}\mspace{14mu} {mod}\mspace{11mu} N_{restrict}} )\Pi_{R \times R}^{k}}}} & \lbrack {{Equation}\mspace{20mu} 33} \rbrack\end{matrix}$

Where N_(restrict) ^(R) is denoted by the number of precoding matrixesof codebook subset determined according to the spatial multiplexing rateR. Thereby, in case that precoding matrixes in a codebook adapted by thecodebook subset limitation scheme are used by cyclic repeated, a systemperformance and the system complexity could be improved.

Fifth Embodiment-2

According to Channel Coding Rate

The codebook subset can be determined differently according to thechannel coding rate. For example, generally, frequency diversity gaincan be increased when channel coding rate is low. Therefore, in the samespatial multiplexing rate circumstance, codebook subset having differentprecoding matrixes, preferably precoding matrixes in low channel codingrate can be used, such that a system performance and the systemcomplexity could be improved.

Fifth Embodiment-3

According to Retransmission

The codebook subset can be determined differently according toretransmission. For example, a codebook subset used at retransmissionhas precoding matrixes different with precoding matrixes of codebooksubset had used at the initial transmission. That is, according towhether to retransmit or the number of retransmission, and so on,differently composed codebook subset can be used. Thereby, the successrate of the retransmission can be increased.

Seventh Embodiment

Extension of Generalized Phase Shift Diversity for Power Control PerTransmission Antenna

As to various precoding schemes, different power values per TX antennacan be used in variation of frequency or time. Thereby, systemperformance may be increased and effective power usage is possible. Forexample, power control per Tx antenna is able to be used with theprecoding schemes of Equations 28, 30, 31 and 32.

Especially, the example of Equation 31 using a codebook including N_(c)precoding matrixes is represented by the following Equations 34:

$\begin{matrix}{{{P_{N_{t} \times R} = \{ {P_{N_{t} \times R}^{0},P_{N_{t} \times R}^{1},\ldots \mspace{11mu},P_{N_{t} \times R}^{N_{c} - 1}} \}},{{GPSD}_{N_{t} \times R}^{k} = {{D_{N_{t} \times N_{t}}^{m}(t)}( P_{N_{t} \times R}^{{\lceil\frac{k}{v}\rceil}\mspace{11mu} {mod}\mspace{11mu} N_{c}} )\Pi_{R \times R}^{k}}},{{{or}\mspace{20mu} {GPSD}_{N_{t} \times R}^{k}} = {{D_{N_{t} \times N_{t}}^{m}(t)}( P_{N_{t} \times R}^{{\lfloor\frac{k}{v}\rfloor}\mspace{11mu} {mod}\mspace{11mu} N_{c}} )\Pi_{R \times R}^{k}}}}{{D_{N_{t} \times N_{t}}^{m}(t)} = \begin{pmatrix}{a_{1}^{m}(t)} & 0 & \ldots & 0 \\0 & {a_{2}^{m}(t)} & \ldots & 0 \\\vdots & \vdots & ⋰ & 0 \\0 & 0 & \ldots & {a_{N_{t}}^{m}(t)}\end{pmatrix}}} & \lbrack {{Equation}\mspace{20mu} 34} \rbrack\end{matrix}$

In Equation 34, Π_(R×R) ^(k) is adapted to mix data streams, and mayalso be called a rotation matrix and, Π_(R×R) ^(k) may also be easilyrepresented by the equation 29. And, D_(N) _(t) _(×R) _(t) ^(m) (t) isdenoted by a power control diagonal matrix to enable for each TX antennato transmit a data stream with different power according to m-thfrequency region and/or t-time. α_(N) _(t) ^(m) (t) is denoted by apower control element used in i-th Tx antenna, m-th frequency regionand/or t-time.

The example of Equation 32 using a codebook includingN_(restrict)({≦N_(c)) precoding matrixes is represented by the followingEquations 35:

$\begin{matrix}{\begin{matrix}{P_{N_{t} \times R}^{restrict} = \{ {P_{N_{t} \times R}^{0},P_{N_{t} \times R}^{2},P_{N_{t} \times R}^{3}\mspace{11mu},P_{N_{t} \times R}^{5}} \}} \\{= W_{N_{t} \times R}} \\{= {\{ {W_{N_{t} \times R}^{0},W_{N_{t} \times R}^{2},W_{N_{t} \times R}^{3}\mspace{11mu},W_{N_{t} \times R}^{5}} \}.}}\end{matrix}{{{GPSD}_{N_{t} \times R}^{k} = {{D_{N_{t} \times N_{t}}^{m}(t)}( P_{N_{t} \times R}^{{\lceil\frac{k}{v}\rceil}\mspace{11mu} {mod}\mspace{11mu} N_{c}} )\Pi_{R \times R}^{k}}},{{{or}\mspace{20mu} {GPSD}_{N_{t} \times R}^{k}} = {{D_{N_{t} \times N_{t}}^{m}(t)}( P_{N_{t} \times R}^{{\lfloor\frac{k}{v}\rfloor}\mspace{11mu} {mod}\mspace{11mu} N_{c}} )\Pi_{R \times R}^{k}}}}{{D_{N_{t} \times N_{t}}^{m}(t)} = \begin{pmatrix}{a_{1}^{m}(t)} & 0 & \ldots & 0 \\0 & {a_{2}^{m}(t)} & \ldots & 0 \\\vdots & \vdots & ⋰ & 0 \\0 & 0 & \ldots & {a_{N_{t}}^{m}(t)}\end{pmatrix}}} & \lbrack {{Equation}\mspace{20mu} 35} \rbrack\end{matrix}$

In Equation 35, each of Π_(R×R) ^(k), D_(N) _(t) _(×N) _(t) ^(m) (t) andα_(N) _(t) ^(m) (t) represents the same one with Equation 34.

Eighth Embodiment

Transceiver for Performing Phase-Shift-Based Precoding

Generally, a communication system includes a transmitter and a receiver.In this case, the transmitter and the receiver may be considered to be atransceiver. In order to clarify a feedback function, a part fortransmitting general data is the transmitter, and the other part fortransmitting feedback data to the transmitter is the receiver.

In a downlink, the transmitter may be a part of a Node-B, or thereceiver may be a part of a user equipment (UE). In an uplink, thetransceiver may be a part of the UE, or the receiver may be a part ofthe Node-B. The Node-B may include a plurality of receivers and aplurality of transmitters. And, the user equipment (UE) may also includea plurality of receivers and a plurality of transmitters.

FIG. 7 is a block diagram illustrating a SCW OFDM transmitter based on aphase-shift-based precoding scheme according to the present invention.FIG. 8 is a block diagram illustrating a MCW OFDM transmitter accordingto the present invention.

Referring to FIGS. 7 and 8, channel encoders 510 and 610, interleavers520 and 620, IFFT (Inverse Fast Fourier Transform) units 550 and 650,and analog converters 560 and 660 and so forth are equal to those ofFIG. 1, so that their detailed description will herein be omitted forthe convenience of description. Only precoders 540 and 640 willhereinafter be described in detail.

The precoder 540 includes a precoding-matrix decision module 541 and aprecoding module 542. The precoder 640 includes a precoding-matrixdecision module 641 and a precoding module 642.

The precoding-matrix decision module (541,641) is configured in the formof a first group of equations 12, 14, and 15 or a second group ofequations 20 and 21, and determines a phase-shift-based precodingmatrix. A detailed method for determining the precoding matrix hasalready been described in the second to fourth embodiments, so that adetailed description thereof will herein be omitted for the convenienceof description. The phase-shift-based precoding matrix based on eitherthe first group of equations 12, 14, and 15 or the second group ofequations 20 and 21 may change a precoding matrix for preventing aninterference between sub-carriers, a phase angle of a diagonal matrix,and/or a unitary matrix in time, as shown in Equation 18.

The precoding-matrix decision module (541,641) may select at least oneof the precoding matrix and the unitary matrix on the basis of feedbackinformation of a reception end. In this case, it is preferable that thefeedback information may include a matrix index of a predeterminedcodebook.

The precoding module (542,642) multiplies an OFDM symbol by thedetermined phase-shift-based precoding matrix, and performs precoding onthe multiplied result.

Generally, individual components of a receiver have functions oppositeto those of the transmitter. The receiver in a MIMO-OFDM system using aphase-shift-based precoding matrix will be described.

First, the receiver receives pilot signal from the transmitter andachieves MIMO channel information using the received pilot signal. Andthen, the receiver achieves equivalent MIMO channel information bymultiplying a phase-shift-based precoding matrix by the achieved MIMOchannel information. The phase-shift-based precoding can be determinedbased on at least one of spatial multiplexing rate (or rank) informationand precoding matrix information from the transmitter.

The receiver can extract data signal using the equivalent MIMO channelinformation and signal vector received from the transmitter. And channeldecoding is performed to the extracted data signal for errordetection/correction then, finally data transmitted by the transmittercan be achieved. According to MIMO reception scheme, pre-describedoperations can be used iteratively or additional decoding operations canbe comprised further.

The receiver based on a phase-shift-based precoding scheme according tothe present invention may be adapted without modification in conformitywith the MIMO reception scheme, thereby, further details on the MIMOreception scheme are abridged.

It should be noted that most terminology disclosed in the presentinvention is defined in consideration of functions of the presentinvention, and can be differently determined according to intention ofthose skilled in the art or usual practices. Therefore, it is preferablethat the above-mentioned terminology be understood on the basis of allcontents disclosed in the present invention.

It will be apparent to those skilled in the art that variousmodifications and variations can be made in the present inventionwithout departing from the spirit or scope of the invention. Thus, it isintended that the present invention cover the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

INDUSTRIAL APPLICABILITY

As apparent from the above description, the present invention provides aphase-shift-based precoding scheme for solving the problems ofconventional CDD, PSD, and precoding methods, resulting in theimplementation of effective communication. Specifically, thephase-shift-based precoding scheme is generalized or extended, thedesign of a transceiver is simplified or the communication efficiencyincreases.

Although the preferred embodiments of the present invention have beendisclosed for illustrative purposes, those skilled in the art willappreciate that various modifications, additions and substitutions arepossible, without departing from the scope and spirit of the inventionas disclosed in the accompanying claims.

1. A method for transmitting a data in a Multi-Input Multi-Output (MIMO)system using a plurality of sub-carriers, the method comprising:determining a precoding matrix as a part of a phase-shift-basedprecoding matrix; determining a first diagonal matrix for a phase shiftas a part of the phase-shift-based precoding matrix; determining aunitary matrix as a part of the phase-shift-based precoding matrix; andprecoding by multiplying the phase-shift-based precoding matrix by atransmission symbol per resource, wherein the phase-shift-basedprecoding matrix is determined by multiplying the precoding matrix, thefirst diagonal matrix, and the unitary matrix.
 2. The method accordingto claim 1, wherein: the precoding matrix is selected to becyclic-repeated in a first codebook according to the resource index (k).3. The method according to claim 1, wherein: the precoding matrix isselected to be cyclic-repeated in a first codebook according to theresource index with being repeated by a predetermined unit.
 4. Themethod according to claim 3, wherein: the predetermined unit isdetermined in consideration of the spatial multiplexing rate.
 5. Themethod according to claim 2, wherein: the precoding matrix is selectedfrom a part of the first codebook.
 6. The method according to claim 2,wherein: the precoding matrix is selected from a second codebookcomprising a part of the first codebook.
 7. The method according toclaim 1, wherein: the phase-shift-based precoding matrix is representedby a following equation: $\begin{matrix}{( {\mathbb{P}}_{N_{t} \times R} )\begin{pmatrix}^{{j\theta}_{1}k} & 0 & \ldots & 0 \\0 & ^{{j\theta}_{2}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & \vdots \\0 & 0 & \ldots & ^{{j\theta}_{R}k}\end{pmatrix}( _{R \times R} )} & \lbrack{Equation}\rbrack\end{matrix}$ where (PN_(t)×R) is the precoding matrix, N_(t) is anumber of TX antenna, (UR×R) is the unitary matrix, “k” is a resourceindex is a phase angle value, and R is a spatial multiplexing rate. 8.The method according to claim 1, further comprising: determining asecond diagonal matrix for a phase shift as a part of thephase-shift-based precoding matrix, in which the phase-shift-basedprecoding matrix is determined by multiplying the second diagonalmatrix, the precoding matrix, the first diagonal matrix, and the unitarymatrix.
 9. The method according to claim 2, wherein: the precodingmatrix is selected from the first codebook on a basis of feedbackinformation received from a reception end.
 10. A transceiver fortransmitting a data in a Multi-Input Multi-Output (MIMO) system using aplurality of sub-carriers, the transceiver comprising: aprecoding-matrix decision module which determines a precoding matrix asa part of a phase-shift-based precoding matrix, determines a firstdiagonal matrix for a phase shift as a part of the phase-shift-basedprecoding matrix, determines a unitary matrix as a part of thephase-shift-based precoding matrix,and determines the phase-shift-basedprecoding matrix by multiplying the precoding matrix, the first diagonalmatrix, and the unitary matrix; and a precoding module for precoding bymultiplying the phase-shift-based precoding matrix by a transmissionsymbol per resource.
 11. The method according to claim 10, wherein: theprecoding matrix is selected to be cyclic-repeated in a codebookaccording to the resource index (k).
 12. The transceiver according toclaim 10, wherein: the precoding matrix is selected by modulo-operatingan index (k) of a corresponding sub-carrier with a codebook size (N).13. The transceiver according to claim 10, wherein: thephase-shift-based precoding matrix is represented by a followingequation: $\begin{matrix}{( {\mathbb{P}}_{N_{t} \times R} )\begin{pmatrix}^{{j\theta}_{1}k} & 0 & \ldots & 0 \\0 & ^{{j\theta}_{2}k} & \ldots & 0 \\\vdots & \vdots & ⋰ & \vdots \\0 & 0 & \ldots & ^{{j\theta}_{R}k}\end{pmatrix}( _{R \times R} )} & \lbrack{Equation}\rbrack\end{matrix}$ where (PN_(t)×R) is the precoding matrix, N_(t) is anumber of TX antenna, (UR×R ) is the unitary matrix, “k” is a resourceindex, θ_(i) (i=1, 2, 3, 4) is a phase angle value, and R is a spatialmultiplexing rate.
 14. The transceiver according to claim 10, wherein:the precoding-matrix decision module determines a second diagonal matrixfor a phase shift as a part of the phase-shift-based precoding matrix,in which the phase-shift-based precoding matrix is determined bymultiplying the second diagonal matrix, the precoding matrix, the firstdiagonal matrix, and the unitary matrix.
 15. The transceiver accordingto claim 11, wherein: the precoding matrix is selected on a basis offeedback information received from a reception end.
 16. The transceiveraccording to claim 15, wherein: the feedback information includes aprecoding matrix index(PMI) associated with the codebook.
 17. A methodfor receiving a data in a Multi-Input Multi-Output (MIMO) system using aplurality of sub-carriers, the method comprising: determining aprecoding matrix as a part of a phase-shift-based precoding matrix;determining a first diagonal matrix for a phase shift as a part of thephase-shift-based precoding matrix; determining a unitary matrix as apart of the phase-shift-based precoding matrix; and decoding atransmission symbol per resource based on the phase-shift-basedprecoding matrix, wherein the phase-shift-based precoding matrix isdetermined by multiplying the precoding matrix, the first diagonalmatrix, and the unitary matrix.
 18. The method according to claim 17,wherein: the precoding matrix is selected to be cyclic-repeated in acodebook according to the resource index.
 19. A method for transmittinga data in a Multi-Input Multi-Output (MIMO) system using a plurality ofsub-carriers, the method comprising: determining a precoding matrix, asa part of a phase-shift-based precoding matrix; determining a rotationmatrix according to a spatial multiplexing rate as a part of thephase-shift-based precoding matrix; and precoding by multiplying thephase-shift-based precoding matrix by a transmission symbol perresource, wherein the phase-shift-based precoding matrix is determinedby multiplying the precoding matrix and the rotation matrix.
 20. Themethod according to claim 19, wherein: the precoding matrix is selectedfrom a part of a first codebook.
 21. The method according to claim 19,wherein: the precoding matrix is selected from a second codebookcomprising a part of a first codebook.
 22. The method according to claim21, wherein: the second codebook is determined in consideration of atleast one of the spatial multiplexing rate, channel coding rate andretransmission.
 23. The method according to claim 17, wherein: therotation matrix comprises a product of a diagonal matrix for a phaseshift and an unitary matrix.
 24. The method according to claim 17,wherein: the precoding matrix is selected to be cyclic-repeated in afirst codebook according to the resource index with being repeated by apredetermined unit.
 25. The method according to claim 24, wherein: thepredetermined unit is determined in consideration of the spatialmultiplexing rate.
 26. The method according to claim 19 or 20, furthercomprising: determining a diagonal matrix for a power control as a partof the phase-shift-based precoding matrix, in which thephase-shift-based precoding matrix is determined by multiplying theprecoding matrix, the rotation matrix and the diagonal matrix for apower control.